The parametric Doppler effect in a medium with Lorentz dispersion

The frequency conversion under the parametric Doppler effect, which occurs when weak probe radiation reflects off from a refractive index inhomogeneity induced in a nonlinear medium by intense pumping, has been analyzed. Under these conditions, the frequency dispersion of the medium is assumed to correspond to the single Lorentz oscillator model. It is shown that the presence of resonance and a spectral range forbidden for propagation may lead to a complex Doppler effect, where the incident radiation is single-frequency but the reflected radiation consists of two or three monochromatic waves, one of which has a phaseconjugated wavefront.     

Transformation of electromagnetic radiation by rapidly moving inhomogeneities of a transparent medium

A theory of reflection and transmission of electromagnetic radiation by inhomogeneities of the parameters of a static transparent medium moving at the velocity of light is developed. Expressions are obtained for the Doppler frequency shift of radiation; it turns out that, under the condition of pronounced frequency dispersion, the frequency of incident radiation corresponds to two frequencies of reflected radiation (complementary waves). It is found that, as the velocity of an inhomogeneity tends to the phase velocity of radiation in the medium, the reflection and transmission coefficients of radiation by the inhomogeneity indefinitely increase. It is shown that the electromagnetic radiation frequency may increase severalfold, with a transformation coefficient of about unity, due to the Doppler shift by the inhomogeneities of a nonlinear medium that are induced by pulses (solitons) of intense counterpropagating radiation.     

The parametric Doppler effect upon oblique incidence of probe radiation

Transformation of frequency and intensity of probe radiation obliquely incident on a moving inhomogeneity induced by an intense laser radiation in a nonlinear medium is analyzed. The dependences of frequency and intensity of radiation reflected from the inhomogeneity have been found for a variant of frequency dispersion corresponding to collision-free plasma. These dependences possess singularities under conditions corresponding to the Vavilov-Cherenkov effect. The initially weak noise components of probe radiation increase in the reflected radiation up to a considerable value.     

Forward light reflection from a moving inhomogeneity

The reflection of monochromatic and quasi-monochromatic pulsed light incident on a moving inhomogeneity in the optical characteristics of a medium having plasma-type dispersion has been analyzed. The velocity V of the inhomogeneity, induced in the medium by an intense laser pulse, has been changed by varying its carrier frequency. It has been shown that the usual back-reflection mode, when the reflected radiation pulse moves in the direction opposite the direction of incident radiation, is implemented only if the velocity V is less than the critical value V _min, which depends on the carrier frequency of the incident radiation pulse. It has been found that reflected radiation moves in the same direction as the incident radiation in a certain range of the velocity V _min < V < V _max (forward reflection). In this case, the reflected radiation pulse begins to lag behind a fast-moving inhomogeneity. When V _max < V < c, where c is the speed of light in vacuum, the group velocity of the incident radiation pulse is less than the speed of inhomogeneity, and there is no reflection. Analytical treatment is supported by numerical simulation.     

Complex resonance in Fresnel reflection of radiation pulses

The Fresnel reflection of radiation pulses with an exponential temporal amplitude profile is analyzed. The conditions for the relevance of the concept of reflectance at a complex frequency, the imaginary part of which determined the rate of time variation of the amplitude, are specified. For the radiation pulses under study, we demonstrate a complex resonance, i.e., an increase in the magnitude of reflectance for the complex frequency of incident radiation (trailing edge of a pulse) that approaches the complex frequency of natural oscillations of oscillators in the medium.     

Complex resonance and complex-frequency spectroscopy

The response of a medium to radiation with a complex frequency corresponding to an exponential time decrease in the radiation amplitude has been analyzed. The effect of complex resonance has been demonstrated when the real and imaginary parts of the complex radiation frequency approach the real and imaginary parts of the complex frequency of damping natural oscillations of medium oscillators. In resonance itself, the absolute value of the refractive index is divergent and radiation is completely reflected from the medium boundary. It has been shown that scanning of not only the real part, but also the imaginary part of the probe radiation frequency expands the capabilities of spectroscopy and makes it possible to, e.g., distinguish resonances even with coinciding (real) frequencies and close (of the same order of magnitude) widths.     

Nonlinear reflection of a femtosecond spectral supercontinuum

The spatio-temporal spectrum of optical radiation reflected from a nonlinear dielectric medium with nonresonant dispersion is obtained as a function of the parameters of the spatio-temporal spectrum of a paraxial light beam incident on the boundary of the medium at small angles. Nonlinear reflection of various types of femtosecond spectral supercontinua from the interface between air and fused silica is simulated. It is shown that the time duration and the transverse dimensions of a beam of multiple-frequency radiation generated during the reflection of a superposition of high-intensity fields of two few-cycle pulses with different central wavelengths may be smaller than those of incident ultrashort pulses.     

Transformation of a Gaussian pulse reflecting from a nonlinear medium

The transformation of the envelope of a Gaussian pulse incident on and reflecting from a nonlinear dispersive medium is studied. It is shown that the pulse envelope transforms considerably upon reflection near the optical resonance frequency and the nonlinearity of the medium may appreciably distort the reflected pulse. Away from the resonance frequency, conditions may arise when the shift of the reflected pulse does not lead to the loss of the Gaussian form. In this case, the influence of nonlinearity is insignificant.     

超声液位检测频率选择的理论计算和实验研究

非介入式超声液位检测中,中间层介质对反射回波强度有着显著的影响,为得到较强的检测回波信号,发射频率的选择是非常必要的。本文采用传输矩阵方法,对非介入式超声液位检测中声波在多层介质中的传播进行了研究,给出了反射回波声强与入射声波频率之间的关系,从理论上计算得到了最佳入射声波频率。实验结果与理论计算一致,由此为非介入式超声液位检测的频率选择提供了一有效的技术途径。     

High-efficiency frequency-modulation non-redundant scanning of a light beam in a half space

It is shown that a large fraction of the energy of the impinging light beam on a parallel plate grating can be injected into only one transmitted order, which is not the zeroth transmitted order, when the incident angle of the beam and the refractive indices of the lossless dielectric bounding media satisfy the condition of total reflection. This signififies that non-redundant scanning of the radiation transmitted through the grafting can be obtained by varying the frequency of the incident radiation with little of the incident energy being scattered into the reflected orders.     

Coherent backscattering of light by a layer of discrete random medium

We consider the problem of backscattering of light by a layer of discrete random medium illuminated by an obliquely incident plane electromagnetic wave. The multiply scattered reflected radiation is assumed to consist of incoherent and coherent parts, the coherent part being caused by the interference of multiply scattered waves. Formulas describing the characteristics of the reflected radiation are derived assuming that the scattering particles are spherical. The formula for the incoherent contribution reproduces the standard vector radiative transfer equation. The interference contribution is expressed in terms of a system of Fredholm integral equations with kernels containing Bessel functions. The special case of the backscattering direction is considered in detail. It is shown that the angular width of the backscattering interference peak depends on the polar angle of the incident wave and on the azimuth angle of the reflection direction.     

Radiation reflection from an optical inhomogeneity moving in a right- and left-handed medium

The parametric Doppler effect in a medium whose dielectric permittivity and magnetic permeability become negative in some spectral range is analyzed with respect to uniform plane waves. The regime in which the medium is right-handed (the refractive index is positive) for incident radiation and left-handed (the refractive index is negative) for reflected wave is demonstrated. The possibility of the occurrence of additional branches in the dispersion dependences is demonstrated.     

Amplification of electromagnetic radiation by a nonequilibrium plasma unstable against the development of Weibel instability

The reflection of an electromagnetic pulse by a nonequilibrium plasma in which the development of Weibel instability is possible has been studied. An exponentially strong amplification of the reflected signal at the stage of instability development has been found to be possible. The amplification maximum takes place at a radiation frequency comparable to the instability growth rate. A nonequilibrium plasma is shown to be a generator of radiation even after the switch-off of the incident pulse. The described effect of amplification of the reflected signal points, in particular, to a new possibility in mastering the terahertz frequency band.     

Single and double scattering approximations for a two-dimensional cylindrical medium

Large spatial frequency expansions for the source function, radiative flux, and intensity are obtained for an isotropically scattering finite two-dimensional medium exposed to collimated radiation. With these expansions, the single and double scattering results are obtained which are valid at small optical distances away from the incident radiation. Results are presented for a circular disk, exponential distribution and a Gaussian distribution of incident radiation.     

Reflection of ultrashort pulses from the boundary of a Drude-Lorentz medium

Reflection of ultrashort pulses of electromagnetic radiation from the boundary between a vacuum and a Drude-Lorentz medium (a set of classical linear oscillators with a low concentration) is considered. For the case of two incident pulses, the possibility of interference quenching of reflected radiation is revealed. The quenching occurs when the pulse amplitudes satisfy a certain relation and the pulses follow with an appropriate time delay.     

Transformation and shift of a Gaussian light beam upon reflection from a resonant medium

The specific features of the transformation and shift of a Gaussian beam reflected from a resonant absorbing medium are analyzed numerically. The study is based on the expansion of the field of the incident Gaussian beam into plane-wave components by using the Fourier integral transform. The calculations are performed for a frequency range covering the resonance region. The conditions for the splitting of the profile of the reflected beam and for its negative shift are established.     

Two-dimensional radiative transfer in a cylindrical geometry with anisotropic scattering

Exact integral equations are derived describing the source function and radiative flux in a two-dimensional, radially infinite cylindrical medium which scatters anisotropically. The problem is two-dimensional and cylindrical because of axisymmetric loading. Radially varying collimated radiation is incident normal to the upper surface while the lower boundary has no radiation incident upon it. The scattering phase function is represented by a spike in the forward direction plus a series of Legendre polynomials. The two-dimensional integral equations are reduced to a one-dimensional form by separating variables for the case when the radial variation of the incident radiation is a Bessel function. The one-dimensional form consists of a system of linear, singular Fredholm integral equations of second kind. Other more complex boundary conditions are shown to be solvable by a superposition of this basic Bessel function case. Diffusely incident radiation is also considered.     

On the passage of an extremely short electromagnetic pulse through a ferroelectric layer embedded in a paraelectric

The refraction and reflection of an extremely short pulse of electromagnetic radiation on a layer of a ferroelectric are considered. For an incident pulse, a stationary pulse propagating without distortions in a paraelectric was used. It is shown that low-amplitude pulses undergo a strong reflection at the entrance to a ferroelectric medium and are not recovered after passage through the layer. High-amplitude pulses are reflected to a considerably lesser extent and can turn into a new stationary pulse after passage through the layer of a ferroelectric. The refraction is accompanied by excitation of polarization oscillations localized at the boundaries of the layer. The intensity of these oscillations and the fraction of the reflected wave are significantly different in cases of similar or opposite polarities of the ferroelectric and incident pulse.     

Quantifying elasticity and viscosity from measurement of shear wave speed dispersion

The propagation speed of shear waves is related to frequency and the complex stiffness (shear elasticity and viscosity) of the medium. A method is presented to solve for shear elasticity and viscosity of a homogeneous medium by measuring shear wave speed dispersion. Harmonic radiation force, introduced by modulating the energy density of incident ultrasound, is used to generate cylindrical shear waves of various frequencies in a homogeneous medium. The speed of shear waves is measured from phase shift detected over the distance propagated. Measurements of shear wave speed at multiple frequencies are fit with the theoretical model to solve for the complex stiffness of the medium. Experiments in gelatin phantoms show promising results validated by an independent method. Practical considerations and challenges in possible medical applications are discussed.     

Negative shift of a light beam reflected from the interface between optically transparent and resonant media

The lateral shift of a light beam reflected from the interface between an optically transparent dielectric and a medium for which the frequency dependences of the real and imaginary parts of the permittivity have a resonant form is investigated. At certain radiation frequencies and angles of incidence, a negative displacement of the reflected beam along the interface takes place.